LisMath Seminar 

15/07/2019, 15:00 — 15:30 — Room 6.2.33, Faculty of Sciences of the Universidade de Lisboa
David García-García, LisMath, Faculdade de Ciências, Universidade de Lisboa

Schur averages in random matrix ensembles

There is a well known relation between matrix integrals over the classical Lie groups and the determinants of Toeplitz and Hankel matrices. We generalize this connection to the averages of Schur polynomials over these groups, which correspond to the minors of the underlying Toeplitz and Hankel matrices. We will show how this approach can be exploited to obtain several results in the theory of symmetric functions and representation theory. Some applications to Chern-Simons theory will also be discussed.